Matrix Multiplication
A matrix is a set or real or complex numbers known as elements arranged
in rows and columns to form a rectangular array of numbers to represent
some kind of data. The rows and columns are also known as the dimensions of the
matrix.
The number of rows is indicated by the letter m and the number of columns
is indicated by the letter n, a matrix of such dimensions will be call an
(m × n), read (m by n) matrix. If m=1, then the matrix is known as a row vector,
and if n=1, then the matrix is known as a column vector.
To multiply two matrices, the number of rows in the second matrix must match the
number of columns in the first matrix. This is shown in the Fig to the far
right.
The Fig to the right shows a typical m*n matrix and how the elements are
labeled, each element is suffixed by m and n as in a_{mn}. The Fig
in the middle shows how to multiply two matrices. In the product matrix, each element
is the sum of the elements of a row from the first matrix multiplied by the elements
of a column from the second matrix, colour marked in the middle Fig.
Use the following tool to multiply two matrices.